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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 113}

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\begin{document}

\begin{center}
    \small Fractions décimales, multiplication/division par 10, 100, 1 000, conversions d'unités.
\end{center}
\vspace{0.5em}
\sloppy

\needspace{5\baselineskip}
\section*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{81}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{55}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 2 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   0,253  ~ \(\times\)  ~ 10
\item   883  ~ \(\times\)  ~ 100
\item   0,014  ~ \(\times\)  ~ 100
\item   5,15  ~ \(\times\)  ~ 100
\item   4,52  ~ \(\times\)  ~ 100
\item   0,207  ~ \(\times\)  ~ 100
\item   9,83  ~ \(\times\)  ~ 1 000
\item   881  ~ \(\times\)  ~ 1 000
\item   36,9  ~ \(\times\)  ~ 1 000
\item   78,8  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 3 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   4,487  ~ : ~ 1 000
\item   768,2  ~ : ~ 100
\item   67,63  ~ : ~ 1 000
\item   324,5  ~ : ~ 1 000
\item   363  ~ : ~ 100
\item   3 032  ~ : ~ 1 000
\item   94,4  ~ : ~ 1 000
\item   222,8  ~ : ~ 10
\item   2,849  ~ : ~ 10
\item   8 562  ~ : ~ 1 000
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 4 : Complète par 10, 100, 1000... :}

\begin{multicols}{2}
\begin{itemize}
\item   0,069  ~ \(\times\)  ~ ... ~ = ~ 0,69
\item   2,28  ~ \(\times\)  ~ ... ~ = ~ 2 280
\item   0,063  ~ \(\times\)  ~ ... ~ = ~ 6,3
\item   151  ~ \(\times\)  ~ ... ~ = ~ 151 000
\item   487  ~ \(\times\)  ~ ... ~ = ~ 487 000
\item   0,096  ~ \(\times\)  ~ ... ~ = ~ 96
\item   0,025  ~ \(\times\)  ~ ... ~ = ~ 0,25
\item   49,3  ~ \(\times\)  ~ ... ~ = ~ 493
\item   65  ~ \(\times\)  ~ ... ~ = ~ 6 500
\item   6,25  ~ \(\times\)  ~ ... ~ = ~ 625
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 5 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   4 007  ~ \(\times\)  ~ 0,001
\item   236,7  ~ \(\times\)  ~ 0,1
\item   814,1  ~ \(\times\)  ~ 0,001
\item   34,33  ~ \(\times\)  ~ 0,01
\item   608,3  ~ \(\times\)  ~ 0,001
\item   353  ~ \(\times\)  ~ 0,01
\item   3,46  ~ \(\times\)  ~ 0,01
\item   946,3  ~ \(\times\)  ~ 0,01
\item   35,85  ~ \(\times\)  ~ 0,1
\item   6,426  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 6 : Complète par 0,1 ~ 0,01 ~  0,001 ... }

\begin{multicols}{2}
\begin{itemize}
\item   5,448  ~ \(\times\)  ~ ... ~ = ~  0,544 8
\item   4,239  ~ \(\times\)  ~ ... ~ = ~  0,423 9
\item   273,9  ~ \(\times\)  ~ ... ~ = ~  27,39
\item   799,5  ~ \(\times\)  ~ ... ~ = ~  7,995
\item   30,41  ~ \(\times\)  ~ ... ~ = ~  0,304 1
\item   80,28  ~ \(\times\)  ~ ... ~ = ~  0,802 8
\item   7,531  ~ \(\times\)  ~ ... ~ = ~  0,753 1
\item   5,937  ~ \(\times\)  ~ ... ~ = ~  0,005 937
\item   37,72  ~ \(\times\)  ~ ... ~ = ~  0,377 2
\item   4 485  ~ \(\times\)  ~ ... ~ = ~  44,85
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 7 : Complète par 10,100 1 000... ou une fraction décimale : }

\begin{multicols}{2}
\begin{itemize}
\item   1 ~cm~ = ...~dam
\item   1 ~dam~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~cm
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 8 : Complète : }

\begin{multicols}{2}
\begin{itemize}
\item   754,47 ~kL~ = ...~mL
\item   409,25 ~dam~ = ...~cm
\item   8 556,7 ~dag~ = ...~hg
\item   1 242,4 ~dm~ = ...~km
\item   241,86 ~kL~ = ...~cL
\item   1 856,1 ~hL~ = ...~dL
\item   6 382,1 ~dm~ = ...~cm
\item   9 257,6 ~daL~ = ...~kL
\item   429,28 ~mL~ = ...~kL
\item   662,4 ~hg~ = ...~kg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

\needspace{5\baselineskip}
\subsection*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{130}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{81}{10}\) = \(\dfrac{810}{100}\)
\item   \(\dfrac{55}{100}\) = \(\dfrac{550}{1\,000}\)
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 2 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   0,253  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,53}
\item   883  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 88 300}
\item   0,014  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,4}
\item   5,15  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 515}
\item   4,52  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 452}
\item   0,207  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 20,7}
\item   9,83  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 830}
\item   881  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 881 000}
\item   36,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 36 900}
\item   78,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 78 800}
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 3 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   4,487 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 487}
\item   768,2 ~ : ~ 100 ~ = ~{\color{red} 7,682}
\item   67,63 ~ : ~ 1 000 ~ = ~{\color{red} 0,067 63}
\item   324,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,324 5}
\item   363 ~ : ~ 100 ~ = ~{\color{red} 3,63}
\item   3 032 ~ : ~ 1 000 ~ = ~{\color{red} 3,032}
\item   94,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,094 4}
\item   222,8 ~ : ~ 10 ~ = ~{\color{red} 22,28}
\item   2,849 ~ : ~ 10 ~ = ~{\color{red} 0,284 9}
\item   8 562 ~ : ~ 1 000 ~ = ~{\color{red} 8,562}
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 4 : Complète par 10, 100, 1000... :}

\begin{multicols}{2}
\begin{itemize}
\item   0,069 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,69
\item   2,28 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 280
\item   0,063 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,3
\item   151 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~151 000
\item   487 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~487 000
\item   0,096 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~96
\item   0,025 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,25
\item   49,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~493
\item   65 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 500
\item   6,25 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~625
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 5 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   4 007 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,007
}\item   236,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 23,67
}\item   814,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,814 1
}\item   34,33 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,343 3
}\item   608,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,608 3
}\item   353 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,53
}\item   3,46 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,034 6
}\item   946,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,463
}\item   35,85 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,585
}\item   6,426 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,064 26
}\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 6 : Complète par 0,1 ~ 0,01 ~  0,001 ... }

\begin{multicols}{2}
\begin{itemize}
\item   5,448 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,544 8
\item   4,239 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,423 9
\item   273,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 27,39
\item   799,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,995
\item   30,41 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,304 1
\item   80,28 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,802 8
\item   7,531 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,753 1
\item   5,937 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 937
\item   37,72 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,377 2
\item   4 485 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 44,85
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 7 : Complète par 10,100 1 000... ou une fraction décimale : }

\begin{multicols}{2}
\begin{itemize}
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 8 : Complète : }

\begin{multicols}{2}
\begin{itemize}
\item   754,47 ~kL~ = {\color{red}  754 470 000 }~mL
\item   409,25 ~dam~ = {\color{red}  409 250 }~cm
\item   8 556,7 ~dag~ = {\color{red}  855,67 }~hg
\item   1 242,4 ~dm~ = {\color{red}  0,124 24 }~km
\item   241,86 ~kL~ = {\color{red}  24 186 000 }~cL
\item   1 856,1 ~hL~ = {\color{red}  1 856 100 }~dL
\item   6 382,1 ~dm~ = {\color{red}  63 821 }~cm
\item   9 257,6 ~daL~ = {\color{red}  92,576 }~kL
\item   429,28 ~mL~ = {\color{red}  0,000 429 28 }~kL
\item   662,4 ~hg~ = {\color{red}  66,24 }~kg
\end{itemize}
\end{multicols}
\end{document}
